Noninvertibility preservers on Banach algebras
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 919-921.

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It is proved that a linear surjection $\Phi \:\mathcal A\rightarrow \mathcal B$, which preserves noninvertibility between semisimple, unital, complex Banach algebras, is automatically injective.
Classification : 46H05, 46H10, 47B48, 47B49
Mots-clés : linear preserver; noninvertible element; semisimple Banach algebra; socle 
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Kuzma, Bojan. Noninvertibility preservers on Banach algebras. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 919-921. https://geodesic-test.mathdoc.fr/item/CMJ_2006__56_3_a9/